7. Here are the number of free throws made by Michigan State's starting point guard Kalin Lucas for 100 simulated rounds of free throws where Kalin Lucas had 20 attempts, assuming he has the ability to hit 82% of his free throws. a) In the 100 simulated rounds, what was the worst performance? Average performance? Best performance? bj In this context, explain what it means to have an 2 10 14 6 18 20 ability of 82%? Simulated Number of Made Free Throws c) Circle a dot on the dotplot. Explain in detail below what this dot represents. d) Suppose that in his next round, Lucas attempts another 20 free throws and makes 8 of them. Would this be a surprising performance? Explain. e) Suppose that he makes 18 out of his next 20 free throw attempts in the next round. Would this be a surprising performance? Explain. f) How many free throws would Kalin Lucas need to make (in a round with 20 attempts) to give you convincing evidence that his ability has decreased? Explain. g) Suppose that you decide that Lucas' ability has changed. What are some plausible causes for this change? 8. I flip a coin and roll a die. I record the outcome of the coin and the die. Are these two events independent? Explain why or why not